Shearing wave

A shearing wave is a local disturbance whose wavevector evolves under background shear. In a Keplerian sheet, $k_x(t)=k_x(0)+(3/2)\Omega k_{y}t$.

The shearing-wave ansatz writes a perturbation as a time-dependent amplitude times $\exp [i{k}_x(t)x+i{k}_{y}y]$, choosing $k_x(t)$ so that background advection does not leave an explicit factor of position in the amplitude equations.

During the swing of a shearing wave, the radial wavenumber passes through zero and the disturbance changes from leading to trailing before winding ever more tightly.